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\begin{equation*}\Gamma(z+1) = z! = \sqrt{2\pi} {\left( z + g + \begin{matrix} \frac{1}{2} \end{matrix} \right)}^{z + \frac{1}{2} } e^{-\left(z+g+\frac{1}{2}\right)} A(z)\end{equation*}
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